[Merged by Bors] - feat: port Topology.PathConnected #2755
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j-loreaux
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Mathbin -> Mathlib fix certain import statements move "by" to end of line add import to Mathlib.lean
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The major thing to note is that I have replaced the `CoeFun` instance (which was `p ↦ p.toContinuousMap.toFun`) with `FunLike.coe`, but previously `Path` did not have a `FunLike` instance, so I have added a `ContinuousMapClass` instance. These are defeq. This also meant there would have been *two* coercions from `Path x y` to `C(I, X)`, namely, the one which was originally declared in this file (`:= p ↦ p.toContinuousMap`) and the one inherited from `ContinuousMapClass`. As a result I have opted for the deleting the former in favor of the latter. These are *not* definitionally equal, but with the rewrite lemmas in place, there seem to be no real issues. Note: the biggest reason for switching to `FunLike` was that the previous coercions were causing absolute hell early in the file with timeouts. If you want to see what I mean, checkout an early commit and attempt to start fixing. Co-authored-by: Moritz Firsching <firsching@google.com>
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The major thing to note is that I have replaced the
CoeFuninstance (which wasp ↦ p.toContinuousMap.toFun) withFunLike.coe, but previouslyPathdid not have aFunLikeinstance, so I have added aContinuousMapClassinstance. These are defeq.This also meant there would have been two coercions from
Path x ytoC(I, X), namely, the one which was originally declared in this file (:= p ↦ p.toContinuousMap) and the one inherited fromContinuousMapClass. As a result I have opted for the deleting the former in favor of the latter. These are not definitionally equal, but with the rewrite lemmas in place, there seem to be no real issues.Note: the biggest reason for switching to
FunLikewas that the previous coercions were causing absolute hell early in the file with timeouts. If you want to see what I mean, checkout an early commit and attempt to start fixing.